1.
2002년도 한국지진공학회 춘계학술발표회
Hybrid Control Strategy for Seismic Protection of Benchmark Cable-Stayed Bridges
박규식, 한국과학기술원 토목공학과 박사과정
정형조, 한국과학기술원 토목공학과 연구조교수
이종헌, 경일대학교 토목공학과 교수
이인원, 한국과학기술원 토목공학과 교수

2. CONTENTS Introduction Benchmark problem statement
Seismic control system using hybrid control strategy
Numerical simulations
Conclusions

3. INTRODUCTION
Many control strategies and devices have been developed and investigated to protect structures against natural hazard.
The control of very flexible and large structures such as cable-stayed bridges is a unique and challenging problem.
The 1st generation benchmark control problem for cable-stayed bridges under seismic loads has been developed (Dyke et al., 2000).

4. Objective of this study:
investigate the effectiveness of hybrid control strategy for seismic protection of cable-stayed bridges under seismic loads
hybrid control strategy:
combination of passive and active control strategies

5. BENCHMARK PROBLEM STATEMENT
Benchmark bridge model
Under construction in Cape Girardeau, Missouri, USA
Sixteen STU* devices are employed in the connection between the tower and the deck in the original design.
STU
STU: Shock Transmission Unit

6. BENCHMARK PROBLEM STATEMENT
Benchmark bridge model
Under construction in Cape Girardeau, Missouri, USA
Sixteen STU* devices are employed in the connection between the tower and the deck in the original design.
128 cables
Two H- shape towers
12 additional piers
STU: Shock Transmission Unit

7. Linear evaluation model
- The Illinois approach has a negligible effect on the
dynamics of the cable-stayed portion.
- The stiffness matrix is determined through a nonlinear
static analysis corresponding to deformed state of the
bridge with dead loads.
- A one dimensional excitation is applied in the longitudinal
direction.
- A set of eighteen criteria have been developed to evaluate
the capabilities of each control strategy.
Control design problem
- Researcher/designer must define the sensor, devices,
algorithms to be used in the proposed control strategy.

8. Historical earthquake excitations
PGA: g
PGA: g
PGA: g

9. Evaluation criteria - Peak responses J1: Base shear
J2: Shear at deck level
J3: Overturning moment
J4: Moment at deck level
J5: Cable tension
J6: Deck dis. at abutment
- Control Strategy (J12 – J18)
J12: Peak force
J13: Device stroke
J14: Peak power
J15: Total power
J16: Number of control devices
J17: Number of sensor
J18:
- Normed responses
J7: Base shear
J8: Shear at deck level
J9: Overturning moment
J10: Moment at deck level
J11: Cable tension

10. SEISMIC CONTROL SYSTEM USING HYBRID CONTROL STRATEGY
Passive control devices
- In this hybrid control strategy, passive control strategy
has a great role for the effectiveness of control
performance.
- Lead Rubber Bearings (LRBs) are used as passive control
devices.

11. - The design of LRBs follows a general and recommended
procedure (Ali and Abdel-Ghaffar, 1995).
: The combined plastic or/and elastic stiffness of the bearings
at the pier or/and bent are assumed to be 1.15M/m.
(M: the part of deck weight carried by bearings)
: The elastic stiffness of LRB is assumed to be 10 times the
plastic stiffness.
: The design shear force level for the yielding of lead plug is
taken to be 0.15M.
- The equivalent linear model for LRB is used.

12. Active control devices
- A total of 24 hydraulic actuator, which are used in the
benchmark problem, are employed.
- The actuators have a capacity of 1000 kN.
- Actuator dynamics are neglected and the actuator is
considered to be ideal.
- five accelerometers and four displacement sensors are used
for feedback.
- An H2/LQG control algorithm is adopted.

13. 24 LRBs, 24 hydraulic actuators
Control devices and sensor locations
H2/LQG
Control force 2 1
5 accelerometers 2
4 displacement sensors 8 4
24 LRBs, 24 hydraulic actuators

14. Control design model (Reduced-order model)
- formed from the evaluation model and has 30 states
- by forming a balanced realization and condensing out the
states with relatively small controllability and observability
grammians
- the resulting state space system is
: State space eq.
: Regulated output eq.
: Measured output eq.

15. Weighting parameters for active control part
- performance index
Q: Response weighing matrix
R: Control force weighting matrix (identity matrix)

16. - the maximum response approach is used.
Step 1. Calculate maximum responses for the candidate
weighting parameters as increasing each parameters.
Step 2. Normalized maximum responses by the results of based
structure and plot sum of max. responses.
Step 3. Select two parameters which give the smallest sum of
max. responses.

17. - the maximum response approach is used.
Step 4. Calculate maximum responses for the selected two
weighting parameters as increasing each parameters
simultaneously.
Step 5. Determine the values of the appropriate optimal
weighting parameters.
Step 1. Calculate maximum responses for the candidate
weighting parameters as increasing each parameters.
Step 2. Normalized maximum responses by the results of based
structure and plot sum of max. respomses.
Step 3. Select two parameters which give the smallest sum of
max. responses.

18. - the selected values of appropriate optimal weighting parameters
: for active control strategy
min. point
bm: base moment
dd: deck dis.

19. : for hybrid control strategy
unstable controller
min.point
bs: base shear
td: top tower dis.

20. NUMERICAL SIMULATIONS
Simulation results
- time history response
deck displacement
base moment (overturning moment)
- evaluation criteria

21. Time history responses under three historical earthquakes

22. Displacement (cm)
Base moment (105 kN·m)

23. Evaluation criteria under El Centro earthquake

24. Evaluation criteria Passive Active Hybrid 0.314 0.271 0.321 0.894
J1. Max. base shear
0.314
0.271
0.321
J2. Max. deck shear
0.894
0.790
0.653
J3. Max. base moment
0.299
0.254
0.309
J4. Max. deck moment
0.443
0.460
0.302
J5. Max. cable deviation
0.170
0.147
0.144
J6. Max. deck dis.
1.184
1.006
0.793
J7. Norm base shear
0.246
0.200
0.237
J8. Norm deck shear
0.728
0.716
0.541
J9. Norm base moment
0.281
0.201
0.244
J10. Norm deck moment
0.391
0.512
0.265
J11. Norm cable deviation
1.31e-2
1.62e-2
1.56e-2
J12. Max. control force
7.82e-3
1.96e-3
4.53e-3
J13. Max. device stroke
0.778
0.660
0.521
J14. Max. power -
4.57e-3
3.76e-3
J15. Total power
7.25e-4
5.96e-4
4.53e-3
LRB: 5.24e-3
HA: 1.96e-3

25. Evaluation criteria under Mexico City earthquake

26. Evaluation criteria Passive Active Hybrid 0.578 0.507 0.546 1.025
J1. Max. base shear
0.578
0.507
0.546
J2. Max. deck shear
1.025
0.910
0.773
J3. Max. base moment
0.768
0.448
0.500
J4. Max. deck moment
0.364
0.415
0.259
J5. Max. cable deviation
4.70e-2
4.50e-2
4.20e-2
J6. Max. deck dis.
2.194
1.666
1.342
J7. Norm base shear
0.503
0.376
0.419
J8. Norm deck shear
0.820
0.770
0.632
J9. Norm base moment
0.579
0.356
0.412
J10. Norm deck moment
0.567
0.691
0.370
J11. Norm cable deviation
5.05e-3
6.27e-3
4.84e-3
J12. Max. control force
3.48e-3
1.22e-3
1.96e-3
J13. Max. device stroke
1.105
0.839
0.676
J14. Max. power -
2.62e-3
1.30e-3
J15. Total power
3.49e-4
1.73e-4
1.96e-3
LRB: 2.33e-3
HA: 9.89e-4

27. Evaluation criteria under Gebze earthquake

28. Evaluation criteria Passive Active Hybrid 0.425 0.414 0.408 0.963
J1. Max. base shear
0.425
0.414
0.408
J2. Max. deck shear
0.963
1.158
0.665
J3. Max. base moment
0.364
0.342
0.387
J4. Max. deck moment
0.526
0.879
0.420
J5. Max. cable deviation
0.101
9.01e-2
8.15e-2
J6. Max. deck dis.
1.207
1.803
0.880
J7. Norm base shear
0.312
0.295
0.299
J8. Norm deck shear
0.876
0.951
0.669
J9. Norm base moment
0.343
0.351
0.311
J10. Norm deck moment
0.489
0.762
J11. Norm cable deviation
6.46e-3
8.90e-3
6.48e-3
J12. Max. control force
5.97e-3
1.96e-3
2.98e-3
J13. Max. device stroke
1.73e-4
0.989
0.482
J14. Max. power -
9.33e-3
5.38e-3
J15. Total power
8.80e-4
5.07e-4
2.98e-3
LRB: 3.99e-3
HA: 1.96e-3

29. Maximum evaluation criteria

30. Evaluation criteria Passive Active Hybrid 0.578 0.507 0.546 1.025
J1. Max. base shear
0.578
0.507
0.546
J2. Max. deck shear
1.025
1.158
0.773
J3. Max. base moment
0.768
0.448
0.500
J4. Max. deck moment
0.526
0.879
0.420
J5. Max. cable deviation
0.170
0.147
0.144
J6. Max. deck dis.
2.194
1.803
1.342
J7. Norm base shear
0.503
0.376
0.419
J8. Norm deck shear
0.876
0.951
0.669
J9. Norm base moment
0.579
0.356
0.412
J10. Norm deck moment
0.567
0.762
0.370
J11. Norm cable deviation
1.31e-2
1.62e-3
1.56e-2
J12. Max. control force
7.82e-3
1.96e-3
4.53e-3
J13. Max. device stroke
1.105
0.989
0.676
J14. Max. power -
9.33e-3
5.38e-3
J15. Total power
8.80e-4
5.96e-3
4.53e-3
LRB: 5.24e-3
HA: 1.96e-3

31. Actuator requirements
Earthquake
Max.
Active
Hybrid
1940
El Centro NS
Force(kN)
1000
Stroke(m)
0.0982
0.0774
Vel. (m/s)
0.5499
0.5208
1985
Mexico City
622.23
504.60
0.0405
0.0326
0.2374
0.1665
1990
Gebze NS
0.1297
0.0633
0.4157
0.3142
Actuator requirement constraints
Force: 1000 kN, Stroke: 0.2 m, Vel.: 1m/sec

32. CONCLUSIONS
A hybrid control control strategy combining passive and active control systems has been proposed for the benchmark bridge problem.
The performance of the proposed hybrid control design is quite effective compared to that of the passive control design and slightly better than that of active control design.
The proposed hybrid control design is more reliable that the active control method due to the passive control part.

33. Thank you for your attention.